The median control chart for process monitoring in short production runs

Abstract

The implementation of the $\overline{X}$ chart requires a large number of samples from an underlying process model, which poses a major problem in short production runs, like in the fast-paced smart manufacturing environment. In this study, the median chart, as a robust alternative to the $\overline{X}$ chart, is used to efficiently monitor the normal or non-normal processes in short production runs. The sensitivity of the median chart is assessed in terms of the truncated average run length (TARL), truncated standard deviation of the run length (TSDRL) and expected TARL criteria. The in-control and out-of-control run length performances of the $\overline{X}$ and the median charts are compared when sampling from non-normally distributed processes in short production runs. It is found that when a non-normal process is in-control, the median chart outperforms the $\overline{X}$ chart, as the latter possesses smaller in-control TARL and higher in-control TSDRL values. In addition, for a non-normal (heavy-tailed) out-of-control process, the median chart prevails over the $\overline{X}$ chart. An illustrative example is given to explain the implementation of the median chart in short production runs.

KEYWORDS:

• Truncated average run length
• Expected truncated average run length
• Truncated standard deviation of the run length
• Median chart
• Short production runs

Additional information

Funding

This research is supported by the Universiti Sains Malaysia, Research University (RUI) grant, number 1001.PMATHS.8011039. This research is conducted while the first author is on sabbatical leave at Universiti Tunku Abdul Rahman (UTAR), Kampar.